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Republican U.S. presidential candidate and former U.S. House Speaker Newt Gingrich waves to the crowd with his wife Calista at right at his South Carolina primary election night rally in Columbia, South Carolina, January 21, 2012. REUTERS/Eric Thayer

Newt Gingrich has won the South Carolina Republican primary, capping off a remarkable comeback for his presidential bid that reshapes the trajectory of the battle for the GOP nomination as the race now heads to Florida and beyond.

The results mark the end of a tumultuous week in politics that saw Gingrich erase and then overcome the lead former Massachusetts Governor Mitt Romney had in the Palmetto State following his victory in the Jan. 10 New Hampshire primary. Gingrich came on strong in the closing days of the campaign, looking to rally under his banner the many conservatives unwilling to get behind Romney, who had sought to posture himself as the eventual nominee.

"We don't have the kind of money at least one of the candidates has," Gingrich said in his victory remarks. "But we do have ideas and we do have people. And we proved here in South Carolina that people power with the right ideas beats big money."

Gingrich spent most of his speech Saturday night lashing out at "media elites" in New York and Washington, D.C., while castigating President Obama. He leaned on wonky explanations of policy to draw contrasts with the president, whom Gingrich accused of representing values antithetical to "classical" America.

"It's not that I am a good debater. It's that I articulate the deepest-felt values of the American people," said Gingrich, who admitted at a Thursday debate to sometimes thinking in grandiose terms.

Amidst cheers of "Newt can win," Newt Gingrich calls the S.C. race "humbling" and "sobering" to see so many supporters rally behind his political message.

The evening's second-place finisher, Romney, drew on elements of his stump speech, but also started to preview rhetoric that will become part of his pitched case versus Gingrich in Florida's primary on Jan. 31.

"We're now three contests into a long primary season ... We've still got a long way to go, and a lot of work to do," Romney said in his remarks Saturday night.

Gingrich, Romney said, had joined Obama in launching a "frontal assault on free enterprise," referencing the ex-speaker's attack on Romney's record at Bain Capital.

"Those who pick up the weapons of the left today will find them turned against us tomorrow," Romney said. "If Republican leaders want to join this president in demonizing success...then they're not going to be fit to be our nominee."

After finishing second in the South Carolina primary, Mitt Romney says the race is "getting even more interesting," and tells the crowd, "there is so much worth fighting."

The results in South Carolina only raise the stakes for the battle in Florida, a traditionally expensive contest where voting is closed to only registered Republicans, and the winner is awarded all of the delegates.

The Romney campaign is hoping that contest will be its firewall. They appeared poised to make their argument versus Gingrich even more sharply in the state. They circulated a “flashback” video on Saturday reminding voters of the ethics investigation Gingrich had faced during his speakership.

The former speaker made reference to the next primary several times in his victory speech Satuday.

"With your help, we are now moving onto Florida and beyond," he said, later asking for supporters' help in reaching out to Floridians.

Gingrich, who will appear on NBC's "Meet the Press" on Sunday morning, hopes to capitalize there on his finish in South Carolina, which was driven in part by late deciders, who broke decisively in his direction in the last few days of the campaign. That stretch saw two debate performances by Gingrich, on Monday and Thursday nights. Almost two-thirds of voters said the debates were an important factor in their decision, and Gingrich won about half of them.

More broadly, core elements of the GOP base in South Carolina – conservatives, Tea Party supporters and evangelical Christians – broke for Gingrich. And the former speaker even edged Romney in two important constituencies for the former Massachusetts governor: voters who said electability in November was their most important concern in a nominee, and voters who said the economy was their top issue.

The South Carolina results underscore Romney’s lingering inability to overcome skepticism from conservatives about electing him as their standard-bearer against Obama this fall.

Gingrich had erased Romney’s lead by abandoning his previous pledge to wage a “relentlessly positive” campaign. The former speaker eventually embraced a strategy of drawing strong contrasts with Romney and benefited from the negative advertising run on his behalf by a super PAC – a practice Gingrich loudly denounced in Iowa, where he saw his poll numbers collapse amid attacks by a pro-Romney super PAC.

His victory provides, if nothing else, a symbolic imprimatur; the winner of the South Carolina primary has gone on to win the nomination in each Republican primary since the contest’s inception in 1980.

The South Carolina results capped one of the most unpredictable weeks in the presidential campaign thus far, a week that saw two candidates leave the race and the veneer of inevitability the Romney campaign had built for itself erode by the end.

Watch Newt Gingrich's appearance on NBC's "Meet the Press" on Sunday

Recertified results in the Iowa caucuses found that he had actually lost the contest by a handful of votes to former Pennsylvania Sen. Rick Santorum. And Romney has fought to withstand some of the most intense scrutiny he’s faced during the campaign; critics have assailed his private equity career and demanded Romney release his tax returns – demands which only reached a fever pitch after Romney estimated he pays an effective rate of 15 percent of his income in taxes.

Moreover, Romney’s performance in South Carolina will speak volumes about his fractious relationship with movement conservatives. He’s struggled at times to break through a ceiling on his support from those voters, who are skeptical of Romney’s past conversion on abortion rights and his embrace of authorship of a health care law as governor that closely resembles Obama’s 2010 reform law.

Nonetheless, the fact that Gingrich has arrived at the precipice of political resurrection – again – this cycle is itself remarkable.

Political observers had questioned when, not if, he would drop out after suffering missteps at the outset of his campaign that led to the defection of virtually all of his top staff last June. But Gingrich stuck with it and climbed to the top of the polls in Iowa, only to see his numbers implode again after weathering attacks from super PACs and Texas Rep. Ron Paul’s campaign.

In South Carolina, the former speaker has been aided by a variety of factors contributing to his potential comeback. He’s scored major points with voters with a couple of strong debate performances this week, particularly by way of launching acerbic attacks on the media. His angry refusal to answer allegations made by an ex-wife topped headlines coming out of a debate on Thursday – the same day that saw Texas Gov. Rick Perry drop his own campaign and endorse Gingrich.

GOP candidate Rick Santorum talks about the state of the race and reaffirms that he wants to be the voice for those people in America that don't have one in government

The winnowed field (Jon Huntsman also ended his campaign and endorsed Romney), only reduced the number of candidates threatening to divide the anti-Romney vote in South Carolina.

Santorum, crowned the winner of the Iowa caucuses upon further review of the vote totals, had doggedly criticized both Romney and Gingrich in hopes of rallying conservatives behind his unflashy, if consistent, record.

"Three states, three winners -- what a great country," he said in remarks Saturday evening, vowing to continue his campaign through Florida and subsequent nominating contests.